The book by Jolley, Waldram and Wilson, 'The Theory and Design of Illumination Engineering Equipment', published in 1930, contains methods of designing symmetrical and asymmetrical reflectors that are of historical significance for the field of illumination engineering and nonimaging optics. This paper describes the methods that appear to be first revealed in the book, and the legacy of the work for modern day researchers in the fields of illumination engineering and nonimaging optics. This paper concludes that Jolley, Waldram and Wilson (with, perhaps, some help from the insights of Halberstma) were most likely the first to derive a method of reflector design based on the mapping of an input angle of a source into the prescribed output angle of the reflector based on the concept of integrated flux and energy conservation of flux.